本研究是以有限元素法計算具有一中央裂縫的鋁合金平板、以複材補片修補後之裂縫尖端的應力強度因子，並經由最佳化方法找出最小體積的補片尺寸。文中利用有限元素套裝軟體ANSYS進行建模及執行最佳化，藉由計算經修補後之鋁合金平板裂縫尖端的應力強度因子小於所設定的門檻值作為有效修補的限制條件，進而找出一組最小體積的補片尺寸。由最佳化所得的結果得知，對具有裂縫之鋁合金平板的上、下面各以一複材補片的雙補片來修補時，隨著裂縫長度增加，所需的複材補片尺寸會增加；但裂縫到達一定長度後，增加補片尺寸對於減低應力強度因子的效果不大。修補具相同大小之裂縫的鋁板，長方形複材補片的體積較正方形補片小。本研究的結果找出補片的適合尺寸，以達到修補及節省補片材料的成效。而利用單複材補片修補裂縫後所能降低應力強度因子的效果有限，故修補的效果不佳。

In this thesis, finite element analysis is performed for bonded composite patch repair of a centre cracked aluminum sheet to reduce the stress intensity factor at the crack tip, and the minimum volume of composite patch is obtained through an optimization process. The finite-element software ANSYS is used to build the analysis model and to perform optimization. The aim of this research is to find out the minimum volume of composite patch by calculating the stress intensity factor at the crack tip, which should be below the threshold value after repairing. It is found that for double-sided repair of centre cracked aluminum sheet, the volume of composite patch increases as the length of crack increases. For aluminum plates with a crack of the same length, the volume of rectangular patch required is smaller than that of square patch. For single-sided composite-patch repairing, the reduction of the stress intensity factor and the efficacy of repair are not significant.

[1] 翁慶隆、沈賢、柯正忠, 飛機結構膠合修補技術, 中山科學研究所, (1997).
[2] A. A. Baker, “A summary of work on applications of advanced fibre composites at the Aeronautical Research Laboratories Australia”, Composite Structures 9, 11-16 (1978).
[3] R. A. Mitchell, R.M. Woolley, and D. J. Chwirut, “Analysis of composite reinforced cut-outs and cracks”, American Institute of Aeronautics and Astronautics Journal 4, 744-749 (1975).
[4] R. Jones, and R. J. Callinan, “Finite element analysis of patched cracks”, Journal of Structural Mechanics 7, 107-130 (1979).
[5] T. V. R. S. Umamaheswar, and R. Singh, “Modeling of a patch repair to a thin cracked sheet”, Engineering Fracture Mechanics 62, 267-289 (1999).
[6] B. Bachir Bouiadjra, H. Fekirini, B. Serier, and M. Benguediab, “Numerical analysis of the beneficial effect of the double symmetric patch repair compared to single one in aircraft structures”, Computational Material Science 38, 824-829 (2007).
[7] C. H. Wang, L. R. F. Rose, and R. Callinan, “Analysis of out-of-plane bending in one-sided bonded repair”, International Journal of Solids and Structures 35, 1653-1675 (1998).
[8] A. Mahadesh Kumar, and S. A. Hakeem, “Optimum design of symmetric composite patch repair to centre cracked metallic sheet”, Composite Structures 49, 285-292 (2000).
[9] J. J. Schubbe, and S. Mall, “Modeling of cracked thick metallic structure with bonded composite patch repair using three-layer technique”, Composite Structures 45, 185-193 (1999).
[10] C. H. Chue, and J. C. T. Liu, “The effects of laminated composite patch with different stacking sequences on bonded repair”, Composite Engineering 15, 223-230 (1995).
[11] 周文清, 黏著修補技術之補片最佳設計, 國立成功大學機械工程研究所碩士論文, (1994).
[12] P. Papanikos, K. I. Tserpes, G. Labeas, and S. Pantelakis, “Progressive damage modeling of bonded composite repairs”, Theoretical and Applied Fracture Mechanics 43, 189-198 (2005).
[13] ANSYS Structural Analysis Guide, Release 10.0 ANSYS Inc (2005).
[14] R. G. Budynas, Advanced Strength and Applied Stress Analysis, McGraw-Hill, International Edition (1999).
[15] N. E. Dowling, Mechanical Behavior of Materials, Prentice Hall, International Second Edition (2001).
[16] 康淵、陳信吉, ANSYS 入門, 全華科技圖書股份有限公司, (2004).
[17] J. S. Arora, Introduction to Optimum Design, McGraw-Hall, International Edition (2003).
[18] ANSYS Advanced Analysis Techniques Guide, Release 5.7 ANSYS Inc (1994).
[19] M. R. Ayatollahi, and R. Hashemi, “Computation of stress intensity factor ( ) and T-stress for cracks reinforced by composite patching”, Composite Structures 78, 602-609 (2007).
[20] http://www.matweb.com/index.asp?ckck=1